1. Figure Grouping & Classification 🔳

These questions show you groups of figures and ask which one belongs (or doesn't belong). You need to identify the common characteristic that defines each group.

What to Look For in Figure Groups

Number of sides: Triangles (3), Quadrilaterals (4), Pentagons (5), etc.
Number of elements: How many shapes/dots/lines in each figure?
Shading patterns: Solid, hollow, half-shaded, striped
Size: Large vs small elements
Symmetry: Symmetric vs asymmetric figures
Orientation: Pointing up/down/left/right

Common Classification Patterns

Pattern Type	Description	Example
Shape Count	All figures have same number of shapes	Group A: 2 shapes, Group B: 3 shapes
Odd/Even	Count of elements is odd or even	3, 5, 7 dots vs 2, 4, 6 dots
Enclosure	Shape inside another vs outside	Circle inside square vs beside
Line Type	Curved lines vs straight lines	Circles vs triangles
Intersection	Shapes overlapping vs not	Venn diagrams vs separate

Example: Which Figure Belongs to Group A?

Group A: All have an ODD number of sides (triangle-3, pentagon-5, heptagon-7)

Group B: All have an EVEN number of sides (square-4, hexagon-6, octagon-8)

Question: Where does a 9-sided figure belong?

Answer: Group A (9 is odd)

2. Series Completion & Pattern Recognition 🔄

These questions show a sequence of figures and ask you to identify what comes next. The key is finding the transformation rule.

Types of Transformations

Rotational Changes

Clockwise rotation: 45, 90, 180 degrees
Counter-clockwise rotation
Variable rotation (45, 90, 135...)
Different elements rotate differently

Positional Changes

Moving in a direction (up, down, left, right)
Moving in patterns (diagonal, zigzag)
Bouncing off edges
Following a path

Quantity Changes

Adding elements (+1, +2, etc.)
Removing elements
Doubling/halving
Arithmetic sequences

Property Changes

Shading: solid to hollow
Size: growing or shrinking
Shape morphing: circle to square
Color alternation

Pro Tip: Track Multiple Elements Separately

In complex series, different elements may follow different rules. Track each element independently:

Large shape: rotating 90 degrees clockwise
Small shape: moving to next corner
Dot: alternating inside/outside

3. Matrices & Grid Patterns 🔲

These present figures in a 3x3 (or 2x2) grid with one cell missing. You must determine what completes the pattern.

Matrix Analysis Strategy

Row Rule: Look for patterns across each horizontal row
Column Rule: Look for patterns down each vertical column
Diagonal Rule: Sometimes patterns exist diagonally
Whole Grid Rule: Each element appears exactly once in the entire grid

Common Matrix Pattern	Description
Additive	Row 1 + Row 2 = Row 3 (combining elements)
Subtractive	Row 1 - Row 2 = Row 3 (removing common elements)
XOR (Exclusive Or)	Row 3 contains only elements in R1 OR R2, not both
Distribution	Each shape appears once per row AND once per column
Progressive	Gradual transformation across the row/column

Example: Matrix Problem

Pattern: Each row has one circle, one square, one triangle. Each column also has one of each.

Given: Row 3 has circle and triangle. Column 3 has square and triangle.

Answer: The missing cell must be a SQUARE (needed in row 3) - and we can verify column 3 also needs a square. Correct!

4. Analogies (Visual) 🔀

Visual analogies follow the format: A is to B as C is to ? You must identify the relationship between A and B, then apply it to C.

Common Analogy Relationships

Rotation: A rotated becomes B; C rotated becomes ?
Reflection: A flipped horizontally/vertically becomes B
Addition: A + element = B; C + same element = ?
Size Change: A enlarged/reduced becomes B
Shading Change: A's shading pattern changes to B's pattern
Decomposition: A is broken apart to form B

Solving Strategy

Step 1: Identify ALL changes from A to B (there may be multiple)
Step 2: Apply EXACT same changes to C
Step 3: Check that your answer matches one of the choices
Step 4: Verify by checking if the relationship makes sense

5. Spatial Visualization 🧊

These test your ability to mentally manipulate 3D objects and visualize spatial relationships.

Common Spatial Tasks

Cube/Box Folding

Given a flat pattern, which cube can be formed?
Opposite faces can never be adjacent
Track one face as anchor point
Mentally fold step by step

3D Rotation

Same object rotated in 3D space
Check if all visible faces match
Mirror images are NOT rotations
Track a distinctive feature

Cube Folding Tips

Rule of Opposites: In a cross-shaped cube net, the square at the end of each arm is OPPOSITE to the square at the other end of that line.

Adjacent Check: Two squares sharing an edge in the net will be adjacent faces on the cube.

6. Time Management & Strategies 🎯

ACET Abstract Tips

Don't Overthink: First instinct is often correct; trust your pattern recognition
Start Simple: Look for obvious patterns first (count, shape, shading)
Use Elimination: Cross out answers that clearly violate the pattern
Time Limit: If stuck for 30 seconds, mark and move on
Practice Daily: Abstract reasoning improves with exposure

Train Your Brain

Abstract reasoning is a SKILL that improves with practice:

Do IQ test practice problems
Play pattern games (puzzles, Sudoku variants)
Practice with past ACET abstract sections
Time yourself to build speed
Review wrong answers to understand patterns you missed

7. Practice Questions 📋

Q1: Pattern Recognition

Series: 1 dot, 2 dots, 4 dots, 8 dots, ?

Answer: 16 dots (doubling pattern: x2 each time)

Q2: Rotation Pattern

Series: Arrow pointing UP, RIGHT, DOWN, ?

Answer: LEFT (90-degree clockwise rotation each step)

Q3: Figure Classification

Group A: All closed figures (circle, square, triangle)

Group B: All open figures (arc, line, angle)

Question: Where does a horseshoe shape belong?

Answer: Group B (horseshoe is open, not closed)

Abstract Reasoning